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Unformatted text preview: RC circuit with a regression line. Usually this relation is exponential. I then calculated the theoretical time constant using our measurements of capacitance and resistance shown in Table 8 and the following equation: ! th = RC = (992)(1.0 *10 !6 ) = 0.000992 Table 8: Summarizes our theoretical and experimental time constant data. exp (s) 0.00108 th (s) 0.000992 0.000088 % 8.49 Finally, I did the analysis on the RLC circuit. The first thing I did was calculated the theoretical resonant frequency based off our measurements of inductance and capacitance and Equation 2. My findings are summarized in Table 9. fres!th = 1 2! LC (Equation 2) fres!th = 1 = 1591.55 2! (.01)(.000001) Table 9: Summarizes the experimental and theoretical resonances Inductance (H) Capacitance (F) 0.010 0.000001 fres-th (Hz) 1591.55 fres-exp (Hz) 1550 f 41.55 f % 2.64 For the final part of the RLC portion we were asked to find the Quality Factor (Q) of our RLC data. To calculate this we used Equation 3: Q= fres (Equation 3) ( f1 ! f2 ) To calculate f1 and f2 we found their corresponding voltage with V f = Vmax / 2 . Upon calculating the value of Vf, I noticed that we did not obtain any data points as low as that value. So since there were no experimental frequencies that corresponded very accurately to Vf, I used our RLC data to create an accurate quadratic regression. Using this regression, I was able to get fairly accurate measurements of f1 and f2. Q = 1550 / (2707.4 ! 667.558) = 0.75 Table 10: Summarizes the Q data for the RLC circuit Vmax (v) 2.82 Vf (v) 1.994 f1 (Hz) 667.558 f2 (Hz) 2707.4 Q 0.75 4 Conclusion In part 1 of this lab we confirmed Ohm's Law and the linear relationship it represents between current, resistance, and voltage. Our error was under 1.5% meaning that our circuit and data very accurately portrayed Ohm's Law in action and was thus a success. We next tried to use experimental data to calculate the ratio e/kB in a circuit with a diode. After linearizing our data and applying a regression, I found a ratio that was less than 4% error from the theoretical ratio. We thus successfully confirmed that adding a diode to a cir...
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- Spring '13